What is the Mann-Whitney U test?
The Mann-Whitney U test is the non-parametric equivalent of the two-sample t-test. The Mann-Whitney U test is used to compare the medians of two independent groups.
For example, let’s say we want to test whether the median calcium levels in the rainwater of two different cities are the same. So, we can collect the data for 10 days in two different cities and determine the calcium levels present in the rainwater. After that, we can perform a Mann-Whitney U test to determine whether the median calcium levels present in the rainwater in two different cities are statistically different.
Please note that there are certain assumptions of the Mann-Whiteney U test. They are:
1. The observations should be independent of each other. There should be no relation between the two groups.
2. The observations are not normally distributed.
3. The dependent variable should be ordinal or continuous. We should be able to rank the values of the variable.
4. The independent variable should consist of two independent categories or groups.
How to perform the Mann-Whitney U test?
The Mann-Whitney U test is performed in the following way:
1. We first rank the data (e.g., the amount of calcium present in the rainwater of the two cities) of both groups in ascending order.
2. If the data associated with two ranks are the same, we replace the ranks with the average of the ranks. For example, if the data associated with ranks 2, 3, and 4 are the same, we will replace ranks 2, 3, and 4 with the average of the three ranks, i.e., 3.
3. Next, we calculate U1 and U2. If the sample size is less than 20, then U1 and U2 are calculated in the following way: …






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